bio | website | cims.nyu.edu/~bakhtin |
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location | ||
age | ||
visits | member for | 4 years, 3 months |
seen | 15 hours ago | |
stats | profile views | 1,588 |
Probabilistic models and related issues.
Apr 15 |
answered | Invariant measure of Euler-Maruyama Discretisation of an Ito diffusion |
Apr 4 |
answered | Intuition on Lindeberg condition |
Apr 2 |
awarded | Custodian |
Apr 2 |
reviewed | Approve suggested edit on Placing numbers $1,2,\ldots,n^3$ in a cube so that numbers of any two adjacent unit subcube are coprime |
Apr 2 |
awarded | Citizen Patrol |
Apr 1 |
answered | Does $Mv$ converge to i.i.d in some sense? |
Mar 7 |
awarded | Nice Answer |
Feb 26 |
answered | What are the difference between modeling with stochastic differential equations (SDE) and ordinary differential equations (ODE) with a random force? |
Feb 26 |
revised |
Do Random Walks on the Hexagonal Lattice have a limit?
edited body |
Feb 26 |
comment |
Do Random Walks on the Hexagonal Lattice have a limit?
1. Sort of, but not quite. If you are using the version of Donsker's theorem where you interpolate linearly between consecutive positions, then this interpolation applied to only odd (or only even) times will not coincide with your original process: you walk along the edges of the hexagonal lattice, but the new process walks along the edges of a certain triangular lattice. The difference between those processes is small and easy to estimate. 2. SAW is a very different beast. It is not a Markov process and, moreover, SAW of length $n$ is not a continuation of SAW of length $m$ for $n>m$. |
Feb 25 |
answered | Do Random Walks on the Hexagonal Lattice have a limit? |
Feb 13 |
comment |
Approximation to the ratio of a Gaussian CDF to PDF
@domotorp: W.Feller. An Introduction to Probability Theory and its Applications, Vol I and II |
Feb 13 |
comment |
Approximation to the ratio of a Gaussian CDF to PDF
The coefficients on the l.h.s. are chosen so that a certain cancellation occurs when you differentiate the l.h.s. of the second chain of inequalities. |
Feb 13 |
comment |
Approximation to the ratio of a Gaussian CDF to PDF
@domotorp: I don't happen to have Feller's book anywhere around, but I do not see what seems to be a problem. Yes, the first line of inequalities is trivial, but it is only a differential version of the second one. |
Jan 4 |
awarded | Yearling |
Dec 20 |
comment |
A Claim on Typical Voronoi Cells
@MLT: I don't suffer from lack of publications, and this is hardly a way to advertise your project, so I am skeptical. If you think though your project is interesting, email me. |
Dec 20 |
comment |
A Claim on Typical Voronoi Cells
@YoavKallus: your definition implies that $(x_i)_{i\ge 1}$ is a stationary process. This is bad. For instance, this will mean that there will be finite areas containing infinitely many points. |
Dec 20 |
comment |
A Claim on Typical Voronoi Cells
@YoavKallus: If you try to define things precisely you will be in trouble or end up with meaningless statements. For example, what exactly do you mean by "the process is symmetric under relabelling"? In the construction of my answer I start with an arbitrary Poisson configuration and "relabel" it obtaining a labeling that violates the claim. |
Dec 20 |
comment |
A Claim on Typical Voronoi Cells
I am afraid that my example shows that his claim is wrong. |
Dec 20 |
comment |
A Claim on Typical Voronoi Cells
Answering your questions: 1)yes, this is a counterexample. 2) You want to average over all labelings, but on the plane there are infinitely many Poissonian points and infinitely many labelings on them, and there is no natural distribution on them. Of course, you can take a limit over boxes growing to infinity, then you will arrive at some notion of expected average cell size. Comparing individual points in this scheme will not work, their individuality will be lost in the averaging procedure. |